The goat's owner, Mr Alifi, said he surprised the man with his goat and took him to a council of elders.
They ordered the man, Mr Tombe, to pay a dowry of 15,000 Sudanese dinars ($50) to Mr Alifi.
"We have given him the goat, and as far as we know they are still together," Mr Alifi said.
"When I asked him: 'What are you doing there?', he fell off the back of the goat, so I captured and tied him up".
Mr Alifi then called elders to decide how to deal with the case.
"They said I should not take him to the police, but rather let him pay a dowry for my goat because he used it as his wife," Mr Alifi told the newspaper.